Expanding the applicability of multi-photon fluorescence recovery after photobleaching \textit{in vivo} by incorporating convective flow into the recovery model

Multi-photon fluorescence recovery after photobleaching is a well-established microscopy technique used to study diffusion, with expanding applications \textit{in vivo}. We present a new model of fluorescence recovery that explicitly includes the effect of convective flows within a system, thereby improving the efficacy of the technique \textit{in vivo}, where convective flows are omnipresent. We test this ``flow'' model through both simulations and \textit{in vitro} experimentation, and demonstrate the effectiveness of the new model \textit{in vivo}. Our results show that the flow model significantly improves the capabilities of multi-photon fluorescence recovery after photobleaching \textit{in vivo}, by enabling an accurate determination of the diffusion coefficient, even when significant flows are present.